Learn Polish: Cześć Anno, jak się masz?

Because you are speaking directly to her. This triggers the Vocative case (Wołacz). For most feminine names and nouns ending in -a, like Anna, the ending changes to -o when you call out to them or address them.

Can I use Cześć when leaving, or only when arriving?

You can use it for both! Cześć is a very versatile informal word used to say both hi and bye to people you are close with.

Why is the word się used in jak się masz?

In Polish, asking how someone is doing literally translates to asking how they have themselves. The word masz is the you form of the verb mieć (to have), and się means yourself. Together they form the set phrase jak się masz (how are you).

Could I use this exact sentence to ask my boss how they are?

No, this sentence is extremely informal. Both the greeting Cześć and the phrase jak się masz are only used with people you are on a first-name basis with. With a boss or a stranger, you would use a formal greeting like Dzień dobry and use the formal Pan or Pani.